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EXHIBIT 4-6: Uncerta<strong>in</strong>ty Example for Statistical Sampl<strong>in</strong>g, cont<strong>in</strong>ued<br />

o<br />

For each <strong>in</strong>dividual <strong>gas</strong> compound, the relative <strong>uncerta<strong>in</strong>ty</strong> of the mole%i × MWi is equivalent to the<br />

comb<strong>in</strong>ed reproducibility <strong>and</strong> variability uncerta<strong>in</strong>ties s<strong>in</strong>ce the molecular weight of each <strong>gas</strong><br />

compound is a constant. The aggregated <strong>uncerta<strong>in</strong>ty</strong> associated with the mixture’s MW is calculated<br />

by apply<strong>in</strong>g Equation 4-1, us<strong>in</strong>g the absolute uncerta<strong>in</strong>ties for each molar compound.<br />

∑<br />

2<br />

U ( abs) = U ( abs )<br />

( MW Total )<br />

mole%<br />

× MW<br />

∑<br />

2 2 2<br />

(0.0500× 14.5531) + (0.0564× 1.1517) + (0.0569×<br />

1.6240)<br />

= + (0.0925× 0.3969) + (0.6383× 0.0639) + (0.5025×<br />

0.0814)<br />

+ (0.6685× 0.0216) + (1.0012× 0.0144) + (0.6685×<br />

0.0259)<br />

2 2 2<br />

2 2 2<br />

=<br />

2<br />

(0.7281) + (0<br />

.0650) + (0.0924) + (0.0367) + (0.0408) + (0.0409)<br />

+ (0.0145) + (0.0144) + (0.0173)<br />

2 2 2 2 2<br />

2 2 2<br />

0.7404<br />

Urel ( ) = × 100% = 4.13%<br />

∑( MW Total )<br />

17.9329<br />

= 0.7404<br />

o<br />

The weight percent carbon of the average composition is calculated by apply<strong>in</strong>g the follow<strong>in</strong>g<br />

equation:<br />

Wt% C<br />

∑<br />

lbmole x lbmole C 12 lb C 1<br />

i<br />

Total<br />

= × × ×<br />

100 lbmole<br />

total<br />

lbmolei lbmole C MWTotal<br />

This equates to 71.07% C, as shown <strong>in</strong> Table 4-11.<br />

o<br />

For each compound <strong>in</strong> the <strong>gas</strong> mixture, the <strong>uncerta<strong>in</strong>ty</strong> from this calculation is determ<strong>in</strong>ed by<br />

apply<strong>in</strong>g Equation 4-6, us<strong>in</strong>g the relative uncerta<strong>in</strong>ties of the lbmole i <strong>and</strong> MW Total . This is<br />

demonstrated for the January CH 4 composition.<br />

Urel ( ) = Urel ( ) × Urel ( ) = 5 + 4.13 =6.49%<br />

2 2 2 2<br />

Wt % C i<br />

mole%<br />

i MW Total<br />

o The <strong>uncerta<strong>in</strong>ty</strong> associated with the wt% C of the mixture is calculated by apply<strong>in</strong>g Equation 4-4,<br />

us<strong>in</strong>g the absolute uncerta<strong>in</strong>ties for the weight percent carbon of each molar compound.<br />

∑<br />

2<br />

U ( abs) = U ( abs)<br />

( %)<br />

Wt%<br />

∑ wt<br />

2 2 2<br />

(0.0649× 60.71) + (0.0699× 5.13) + (0.0703×<br />

2.47)<br />

= + × + × + × =<br />

+ (0.6698× 0.10) + (1.0021× 0.07) + (0.6698×<br />

0.12)<br />

3.9724<br />

Urel ( ) = × 100% = 5.59%<br />

∑( Wt %)<br />

71.0717<br />

2<br />

(0.1013 1.81) (0.6397<br />

2<br />

0.29) (0.5042<br />

2<br />

0.37) 3.9734<br />

2 2 2<br />

Pilot Version, September 2009 4-28

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